Restrictions of Békollé--Bonami weights and Bloch functions
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866912722362302464 |
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| author | Dayan, Alberto Llinares, Adrián Perfekt, Karl-Mikael |
| author_facet | Dayan, Alberto Llinares, Adrián Perfekt, Karl-Mikael |
| contents | We characterize the restrictions of Békollé--Bonami weights of bounded hyperbolic oscillation, to subsets of the unit disc, thus proving an analogue of Wolff's restriction theorem for Muckenhoupt weights. Sundberg proved a discrete version of Wolff's original theorem, by characterizing the trace of $BMO$-functions onto interpolating sequences. We consider an analogous question in our setting, by studying the trace of Bloch functions. Through Makarov's probabilistic approach to the Bloch space, our question can be recast as a restriction problem for dyadic martingales with uniformly bounded increments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_04859 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Restrictions of Békollé--Bonami weights and Bloch functions Dayan, Alberto Llinares, Adrián Perfekt, Karl-Mikael Classical Analysis and ODEs Complex Variables Functional Analysis 46E30 (Primary), 30E05, 30H30, 42A61, 47B38 (Secondary) We characterize the restrictions of Békollé--Bonami weights of bounded hyperbolic oscillation, to subsets of the unit disc, thus proving an analogue of Wolff's restriction theorem for Muckenhoupt weights. Sundberg proved a discrete version of Wolff's original theorem, by characterizing the trace of $BMO$-functions onto interpolating sequences. We consider an analogous question in our setting, by studying the trace of Bloch functions. Through Makarov's probabilistic approach to the Bloch space, our question can be recast as a restriction problem for dyadic martingales with uniformly bounded increments. |
| title | Restrictions of Békollé--Bonami weights and Bloch functions |
| topic | Classical Analysis and ODEs Complex Variables Functional Analysis 46E30 (Primary), 30E05, 30H30, 42A61, 47B38 (Secondary) |
| url | https://arxiv.org/abs/2308.04859 |